That applies in particular in the pump described in Document WO 97/23304. The pusher has a push wall on which pressure is exerted by means of a finger for the purpose of actuating the pusher. In addition, the pusher has a skirt that extends downwards from the push wall. Said skirt forms a first leaktight slide cylinder for a differential piston and a main second cylinder for the main piston of the pump. The differential piston is dissociated from the main piston. The differential piston is urged away from the push wall by a spring that serves both as a return spring and as a precompression spring. The slide cylinder for the differential piston is provided with an outlet duct that leads to a nozzle received in a recess formed in the skirt of the pusher. The nozzle forms a dispensing orifice via which the fluid is discharged from the dispenser member. In addition, the recess formed by the skirt is provided with a swirl system which co-operates with the nozzle to entrain the fluid in a swirling movement before it is discharged through the dispensing orifice. The swirl system is conventionally made up of one or more tangential swirl channels opening out into a swirl chamber accurately centered on the dispensing orifice. The swirl system is in the form of a network recessed into the recess in the skirt. The recessed network is then associated with the separate nozzle that comes to isolate the swirl channels and the chamber. Thus, the slide cylinder of the differential piston is in the form of a cylindrical surface interrupted only at the outlet channel. When the pusher is pressed, the main piston rises up inside the main cylinder of the pusher, thereby causing the differential piston to move by sliding in leaktight manner inside the differential cylinder. That causes the spring to be compressed: the differential piston then moves upwards towards the push wall of the pusher. The active sealing lip of the differential piston, which lip is directly in contact with the fluid, slides in the bottom portion of the cylinder that is situated below the outlet channel. As soon as the differential piston reaches the outlet duct, the fluid put under pressure in the chamber is delivered from the chamber through said duct and reaches the nozzle, where it is swirled and discharged through the dispensing orifice.
The pump of Document WO 97/23304 is made up of five essential component elements, namely a body designed to be associated with a fluid reservoir, the pusher, a ball forming an inlet valve member, the differential piston, and the nozzle. The body forms the main piston.
U.S. Pat. No. 4,050,613 describes a pump comprising a pusher and a differential piston which slides within the pusher. The inner wall of the pusher thus forms a slide cylinder. This cylinder is provided with a swirl system which forms a recess in the inner wall of the pusher. Upon sliding in the cylinder, the differential piston unmasks the swirl system. The cylinder is perfectly cylindrical throughout its height and has a constant diameter. The molding step of the swirl system is therefore complicated, because the core used to form the swirl system has to be removed from the cylinder without damaging the cylinder.